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This entry is from Winter semester 2019/20 and might be obsolete. You can find a current equivalent here.

Algebra (for teacher students)
(dt. Algebra (Lehramt))

Level, degree of commitment Advanced module, depends on importing study program
Forms of teaching and learning,
workload		 Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 150 h preparation and follow-up inklusive Studienleistungen, 30 h Vorbereitung and Ablegen von Prüfungsleistungen)
Credit points,
formal requirements		 9 CP
Course requirement(s): Successful completion of at least 50% of the weekly exercises as well as at least 1-3 presentations of the tasks
Examination type: Written examination (90-120 min.)
Language,
Grading		 German,
The grading is done with 0 to 15 points according to the examination regulations for the degree program LAaG Mathematics. In the event of failure, a total of 4 attempts are available for the examination.
Origin LAaG Mathematics
Duration,
frequency		 One semester,
Jedes zweite Semester
Person in charge of the module's outline Prof. Dr. Thomas Bauer, Prof. Dr. István Heckenberger, Prof. Dr. Sönke Rollenske, Prof. Dr. Volkmar Welker

Contents

Groups: Groups and group homomorphisms, subgroups, Lagrange's theorem, normal subgroups and factor groups, isomorphism theorems, cyclic groups, main theorem on finitely generated abelian groups, permutation groups and group actions.

rings: rings and ring homomorphisms, ideals and factor rings, polynomial rings, Euclidean rings, principal ideal domains, divisibility in integral domains, quotient fields, factorial rings, polynomial rings over factorial rings

Fields: fields and field extensions, algebraic and transcendental field extensions


Qualification Goals

Competences:

The students

  • know and use algebraic forms of representation and argumentation and the formal language means of algebra with aplomb,
  • understand basic principles of algebraic structures and recognize that such structures can be found in many parts of mathematics and are profitably applied there,
  • know and use axiomatic procedures,
  • are familiar with the problem of solving algebraic equations, know about the driving force which they represent in the history in algebra, and they know and use the results available for this purpose,
  • have a deeper understanding of the implications and benefits of the algebraic structures such as group, ring and field and can explain the associated results of algebra. They understand concepts such as divisibility and factorization in an abstract context and can also use them in elementary contexts,
  • have basic algebraic knowledge which is required in areas of specialization such as algebraic number theory, algebraic geometry, discrete mathematics, function theory of several variables.

Qualification goals:

Students know and use basic algebraic structures such as groups, rings and fields. They apply algebraic forms of representation and argumentation and understand axiomatic procedures.


Prerequisites

None. The competences taught in the following modules are recommended: Analysis I, Analysis II, Linear Algebra incl. Foundations of Mathematics.


Applicability

The module can be attended at FB12 in study program(s)

  • LAaG Mathematics

When studying LAaG Mathematics, this module must be completed in the study area Advanced Modules.


Recommended Reading

(not specified)



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2019/20. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.